Question

Please help FAST!!
Part 1: Solve each of the quadratic equations below. Show your work. x2 − 16 = 0 and x2 = −2x + 24
Part 2: Describe what the solution(s) represent to the graph of each.
Part 3: How are the graphs alike? How are they different? Thanks for any responses!

Answer 1

\[x ^{2} - 16 = 0\]
Can be written as : \[(x ^{2}- 4^{2}) = 0\]
Now, by using the formula = > \[(a ^{2}-b ^{2}) = (a+b) (a-b)\] ,
we can write the equation as : \[(x+4) (x-4)\] = 0
Therefore, x =+4 or x = -4.

Answer 2

Now, as for the second equation, bring all the terms to one side:
\[x ^{2} + 2x - 24 = 0\]
Now, by using the splitting method / quadratic formula, we get x.
\[x ^{2} - 6x - 4x - 24 = 0\]
\[x(x+6) - 4( x+ 6) = 0\]
\[(x-4) ( x+6) = 0\]
Therefore, x = 4 or x = -6.

Answer 3

Thanks @Jas9420